port-Hamiltonian Model Research Articles

Improved a posteriori error bounds for reduced port-Hamiltonian systems

Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical error bound and (b) an error bound based on an auxiliary linear problem, to the case of port-Hamiltonian systems. The approaches rely on a secondary approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are adapted to port-Hamiltonian systems. The mathematical relationship between the two methods is discussed both theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid–structure interaction.

A Novel Mixed Finite/Infinite Dimensional Port–Hamiltonian Model of a Mechanical Ventilator

Mechanical ventilation is a life-saving treatment for critically ill patients who are struggling to breathe independently due to injury or disease. Globally, per year, there has always been a large number of individuals who have required mechanical ventilation. The COVID-19 pandemic brought to light the significance of mechanical ventilation, which played a significant role in sustaining COVID-19-infected critically ill patients who could not breathe on their own. The pandemic drew the attention of the world to the shortage of ventilators globally. Some of the challenges to providing an adequate number of ventilators include: increased demand for ventilators, supply chain disruptions, manufacturing constraints, distribution inequalities, financial constraints, maintenance and logistics difficulties, training and expertise shortages, and the lack of design and development of affordable mechanical ventilators that satisfy the stipulated requirements. This research work presents the formulation of a detailed Port–Hamiltonian model of a mechanical ventilator integrated with the human respiratory system. The interconnection and coupling conditions for the various subsystems within the mechanical ventilator and the coupling between the mechanical ventilator and the human respiratory system are also presented. Structure-preserving discretization is provided alongside numerical simulations and results. The obtained results are found to be comparable to results presented in the literature. Future work will include the design of suitable controllers for the system.

A systematic methodology for port-Hamiltonian modeling of multidimensional flexible linear mechanical systems

This article introduces a novel systematic methodology for modeling a class of multidimensional linear mechanical systems that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. While the approach is tailored to systems governed by specific kinematic assumptions, it encompasses a wide range of models found in current literature, including ℓ-dimensional elasticity models (where ℓ = 1, 2, 3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology involves formulating the displacement field using primary generalized coordinates via a linear algebraic relation. The non-zero components of the strain tensor are then calculated and expressed using secondary generalized coordinates, enabling the characterization of the skew-adjoint differential operator associated with the port-Hamiltonian representation. By applying Hamilton's principle and employing a specially developed integration by parts formula for the considered class of differential operators, the port-Hamiltonian model is directly obtained, along with the definition of boundary inputs and outputs. To illustrate the methodology, the plate modeling process based on Reddy's third-order shear deformation theory is presented as an example. To the best of our knowledge, this is the first time that a port-Hamiltonian representation of this system is presented in the literature.

Port-Hamiltonian modeling and jumping trajectory tracking control for a bio-inspired quadruped robot

Applying jumping locomotion into autonomous mobile robot is an effective way for improving abilities to overcome barriers and pass through complex terrains. In this paper, based on the designed structural framework for bio-inspired quadruped jumping robot, dynamic model is established by utilizing port-Hamiltonian with dissipation (pHd) method, and a passivity-based control strategy for the robot joints trajectory tracking is presented. First, morphology and biomimetics knowledges of frogs (a kind of animals with excellent jumping skill) motivate us to complete a bio-inspired jumping robot framework based on frog’s motion mechanism and body structure with torsional springs as energy storage device. Then, combining system passivity and dissipation, port-Hamiltonian method is utilized to build a dynamic model for expressing the relationship of energy and force in the designed robot. Jumping process analysis of different stages is also designed for ensuring the robot to complete taking-off and landing stages successfully. Next, with the definition of extending feasible robotic joint trajectory by La Salle invariant set principle, interconnection and damping assignment passivity-based control (IDA-PBC) method is exerted to obtain a trajectory controller for realizing smoothly and stably trajectory tracking in joint space. At last, simulation results show the reasonableness of the designed framework. By comparing our method with state-feedback and sliding mode control, effectiveness of the dynamic model and trajectory controller is also verified.

Energy-optimal control of adaptive structures

Abstract Adaptive structures are equipped with sensors and actuators to actively counteract external loads such as wind. This can significantly reduce resource consumption and emissions during the life cycle compared to conventional structures. A common approach for active damping is to derive a port-Hamiltonian model and to employ linear-quadratic control. However, the quadratic control penalization lacks physical interpretation and merely serves as a regularization term. Rather, we propose a controller, which achieves the goal of vibration damping while acting energy-optimal. Leveraging the port-Hamiltonian structure, we show that the optimal control is uniquely determined, even on singular arcs. Further, we prove a stable long-time behavior of optimal trajectories by means of a turnpike property. Last, the proposed controller’s efficiency is evaluated in a numerical study.

Robustness Analysis on Joint Path-following Control of a Snake-like Robot Using Port-Hamiltonian Model

Robustness Analysis on Joint Path-following Control of a Snake-like Robot Using Port-Hamiltonian Model

Fixed-time [formula omitted] tracking control of unmanned underwater vehicles with disturbance rejection via Port-Hamiltonian framework

The fixed-time tracking control schemes of unmanned underwater vehicles (UUVs) are investigated in body-fixed coordinates frame based on Port-Hamiltonian (PH) model with external disturbances. The novel locally and globally fixed-time control laws via the interconnection and damping assignment passivity-based control (IDA-PBC) are designed for trajectory tracking in UUVs. The virtual desired equilibria consisted of the tracking error and the desired trajectory are established by the matching conditions. Moreover, the fixed-time stabilization of the UUV induced of variable parameter matrixes is analyzed. Compared with the traditional IDA-PBC controller, the UUV is guaranteed to achieve the reference trajectory within a fixed time regardless of initial conditions. In the presence of external disturbances, the H∞ laws are incorporated in the fixed-time control for the UUV, which can ensure faster trajectory tracking and strong anti-disturbance. Finally, the simulation results demonstrate the effectiveness of the main schemes.

Energy-based modeling and robust position control of a dielectric elastomer cardiac assist device

This paper is concerned with the port Hamiltonian modeling and control of a dielectric elastomer actuator used for a cardiac assistance device. The proposed non-linear model is identified under different applied voltages and pressures, and validated against experimental results with relative errors of less than 0.3%. Subsequently, two passivity-based controllers are designed to stabilize the actuator at a desired position. The first controller is designed using control by interconnection. The second one considers additional integral action to reject disturbances while preserving the passivity of the closed-loop system.

Port-Hamiltonian Modeling and Control of Electric Vehicle Charging Stations

Port-Hamiltonian Modeling and Control of Electric Vehicle Charging Stations

Minimal port-Hamiltonian modeling of voice production: choices of fluid flow hypotheses, resulting structure and comparison

Voice production results from the interaction between expelled airflow and soft tissues in the larynx and the vocal tract. Among the large literature on this topic over the last fifty years, a few nonlinear fluid-structure interaction models have been proposed in the port-Hamiltonian framework for passivity purposes. In this paper, we examine, compare and discuss two lumped-element port-Hamiltonian models from the literature, both derived from distributed parameter descriptions and simplifying assumptions chosen to integrate the minimal relevant phenomena involved in the larynx (for self-oscillations) or the vocal tract (during articulation). These models are recalled and reformulated using common terminology and notations. This leads to equivalent circuit representations, the components and the structure of which allow direct comparison (about causality, dimension, nonlinear laws, coupling) and physical interpretation. These results highlight important properties to consider and provide guidelines for future modelling improvement to be used in simulation.

Port-Hamiltonian modeling and control of a curling HASEL actuator

This paper is concerned with the modeling and control of a curling Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator using the port-Hamiltonian (PH) approach. For that purpose, we use a modular approach and consider the HASEL actuator as an interconnection of elementary subsystems. Each subsystem is modeled by an electrical component consisting of a capacitor in parallel with an inductor connected through the conservation of volume of the moving liquid to a mechanical structure based on inertia, linear, and torsional springs. The parameters are then identified, and the model is validated on the experimental setup. Position control is achieved by using Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) with integral action (IA) for disturbance rejection. Simulation results show the Efficiency of the proposed controller.

Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization

This contribution proposes a nonlinear and dissipative infinite-dimensional port-Hamiltonian (PH) model for the dynamics of geometrically exact strings. The mechanical model provides a description of large deformations including finite elastic and inelastic strains in a generalized Maxwell model. It is shown that the overall system results from a power-preserving interconnection of PH subsystems. By using a structure-preserving mixed finite element approach, a finite-dimensional PH model is derived. Eventually, midpoint discrete derivatives are employed to deduce an energy-consistent time-stepping method, which inherits discrete-time dissipativity for the irreversible system. An example simulation illustrates the numerical properties of the present approach.

Port-Hamiltonian Modelling of Complex Non-Linear Systems, Application to a Liquid Propelled Rocket Engine

Port-Hamiltonian (PH) systems theory is a well-established framework for modelling the dynamics of non-linear systems. It has been used extensively for complex mechanical systems. Recent developments have extended this representation to multiphysical systems. In this paper, a PH formulation of a Liquid Propelled Rocket Engine model is proposed. Starting from a classical state-space representation, a new model is derived which allows to demonstrate the global passivity feature of the system using the property of passivity inheritance by composition of several PH subsystems. The resulting representation allows to consider passivity-based control perspective for this class of complex thermodynamics system.

Port-Hamiltonian modeling of a geometrically nonlinear hyperelastic beam

This paper is concerned with the port-Hamiltonian modeling of a Timoshenko beam subject geometric nonlinearities through von Kármán strains, material nonlinearity considering hyperelasticity with the assumption of neo-Hookean or Mooney-Rivlin material, in addition to the incompressible deformation constraint that corresponds to the preservation of volume. The model is suitable for representing the behavior of rubber like beams within the range of moderate deformations and rotations. Numerical simulations are carried out to illustrate the accuracy of the proposed model.

Port-Hamiltonian modeling of large-scale curling HASEL actuators

Port-Hamiltonian modeling of large-scale curling HASEL actuators

Adaptive Path-Tracking Control With Passivity-Based Observer by Port-Hamiltonian Model for Autonomous Vehicles

Adaptive Path-Tracking Control With Passivity-Based Observer by Port-Hamiltonian Model for Autonomous Vehicles

Direct Power Control of a Shunt Active Power Filter Using a Modified IDA–PBC Approach With Integral Action

A direct power based controller designed using a modified interconnection and damping assignment passivity-based control (IDA-PBC) with integral action is proposed in this paper for a shunt active power filter (SAPF). A power based model of the SAPF is proposed and it is described as a port-Hamiltonian model. Then, an extended port Hamiltonian system is proposed including an integral action to compensate for parameter errors and unmodeled uncertainties. From this model, a complete matching equation for the extended system is proposed, and a modified IDA-PBC with integral action is employed to design a power-based controller for a SAPF.

Port-Hamiltonian fluid–structure interaction modelling and structure-preserving model order reduction of a classical guitar

ABSTRACT A fluid–structure interaction model in a port-Hamiltonian representation is derived for a classical guitar. After discretization, we combine the laws of continuum mechanics for solids and fluids within a unified port-Hamiltonian (pH) modelling approach by adapting the equations through an appropriate coordinate transformation on the second-order level. The high-dimensionality of the resulting system is reduced by model order reduction. The article focuses on pH-systems in different state transformations, a variety of basis generation techniques as well as structure-preserving model order reduction approaches that are independent from the projection basis. As main contribution, a thorough comparison of these method combinations is conducted. In contrast to typical frequency-based simulations in acoustics, transient time simulations of the system are presented. The approach is embedded into a straightforward workflow of sophisticated commercial software modelling and flexible in-house software for multi-physics coupling and model order reduction.

Stability and asymptotic analysis for instationary gas transport via relative energy estimates

We consider the transport of gas in long pipes and pipeline networks for which the dynamics are dominated by friction at the pipe walls. The governing equations can be formulated as an abstract dissipative Hamiltonian system which allows us to derive perturbation bounds via relative energy estimates using a problem adapted nonlinear analysis. As particular consequences of these results, we are able to prove stability estimates with respect to initial conditions and model parameters and we conduct a quantitative asymptotic analysis in the high friction limit. Our results are established first for the flow in a single pipe and we then extend our analysis to pipe networks in the spirit of energy-based port-Hamiltonian modelling.

Time-domain Dynamic State Estimation for Unbalanced Three-phase Power Systems

In this paper, we present a time-domain dynamic state estimation for unbalanced three-phase power systems. The dynamic nature of the estimator stems from an explicit consideration of the electromagnetic dynamics of the network, i.e., the dynamics of the electrical lines. This enables our approach to release the assumption of the network being in quasi-steady state. Initially, based on the line dynamics, we derive a graph-based dynamic system model. To handle the large number of interacting variables, we propose a port-Hamiltonian modeling approach. Based on the port-Hamiltonian model, we then follow an observer-based approach to develop a dynamic estimator. The estimator uses synchronized sampled value measurements to calculate asymptotic convergent estimates for the unknown bus voltages and currents. The design and implementation of the estimator are illustrated through the IEEE 33-bus system. Numerical simulations verify the estimator to produce asymptotic exact estimates, which are able to detect harmonic distortion and sub-second transients as arising from converter-based resources.